A Revised Concept of Safety for General Answer Set Programs

Abstract

Abstract.Some answer set solvers deal with programs with variables by requiring a safety condition on program rules. This ensures that there is a close relation between the answer sets of the program and those of its ground version. If we move beyond the syntax of disjunctive programs, for instance by allowing rules with nested expressions, or perhaps even arbitrary first-order formulas, new definitions of safety are required. In this paper we consider a new concept of safety for formulas in quantified equilibrium logic where answer sets can be defined for arbitrary first-order formulas. The new concept captures and generalises two recently proposed safety definitions: that of Lee, Lifschitz and Palla (2008) as well as that of Bria, Leone and Faber (2008). We study the main metalogical properties of safe formulas.

A Free Logic for Stable Models with Partial Intensional Functions

“…The term "free" logic refers to a family of formalisms where syntactic terms may denote objects that are outside the domain of quantification, something that can be used to capture partial functions. 10 We show that this feature can be naturally accommodated 9 In fact, as explained in [4], the difference total/partial between the two semantics is not essential. In Cabalar's semantics, any function can always be forced to be total by adding an axiom ¬¬∃y f (x) = y.…”

“…This syntactic form is called c-plain in [4] and there it was shown that both BL and Cabalar's semantics coincide for this form of theory, under the assumption of total functions. 9 Unfortunately, the unfolding transformation (2) is not safe in BL semantics and the question whether any theory can be equivalently reduced to c-plain form under BL is still unanswered.…”

Stability, Supportedness, Minimality and Kleene Answer Set Programs

“…When rules allow for more complex expressions, different versions of safety are considered [7]. On the other hand, when we fix domains as finite sets of constant symbols, the problems related to non-safety disappear.…”

Disjunctive logic programs with existential quantification in rule heads

“…Answer set programming (ASP) has been generalized from normal logic programming (Gelfond and Lifschitz 1988) to arbitrary first-order sentences (Ferraris et al 2011). Some classes of programs in this context have been studied and properties revealed (e.g., (Lee et al 2008;Cabalar et al 2009; Bartholomew and Lee 2010; Lee and Meng 2011; Lee and Palla 2012)). In this paper, we consider (firstorder) disjunctive logic programs without function symbols but with existential quantification (EQ) in rule heads, which we call E-disjunctive programs (or just E-programs).…”

“…Another issue is decidability. Non-trivial E-disjunctive programs fall outside of any known decidable classes of safe logic programs (Cabalar et al 2009;Bartholomew and Lee 2010).…”